Model Name: iMac
Model Identifier: iMac7,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache (per processor): 4 MB
Memory: 1 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version: 1.20f4
Serial Number: not telling
Does this help...
Yes, that does help. That iMac can currently run the latest verison of Mac OS X and 10.9. To do that, you need to get a Snow Leopard/10.6 disc from Apple and install that. Then you need to buy Mountain Lion/10.8 from the App Store. I also highly recommend upgrading your memory to 4GB as 10.8 and even 10.6 on 1GB of memory is a bit slow.
Yes, the disc is required. Snow Leopard costs $20 new from Apple. Then Mountain Lion is another $20. Lion is 10.7 and Leopard is 10.5. You can skip both of those, but Snow Leopard is needed to go to anything beyond it because it has access to the Mac App Store where you purchase and download 10.7+.
Lion/Mtn Lion require 2GB RAM. You should be able to upgrade to 10.6 no problem, which is still more or less supported, but if you want to get current you'll need a RAM upgrade.